MATHEMATICA BOHEMICA, Vol. 130, No. 1, pp. 101-105 (2005)

All graphs in which each pair of distinct vertices has exactly two common neighbors

Dragan Stevanovic

Dragan Stevanovic, Faculty of Science and Mathematics, Visegradska 33, 18000 Nis, Serbia and Montenegro, e-mail:

Abstract: We find all connected graphs in which any two distinct vertices have exactly two common neighbors, thus solving a problem by B. Zelinka.

Keywords: graphs, adjacency matrix, eigenvalues of a graph, common neighbours

Classification (MSC2000): 05C75, 05C50

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